What you can do is have Layer 1, 2, 3 close together. All your fast edges would be contained on the top layer, so that you have access to a reference plane and have the coveted inter-plane capacitance.
And layer 4 would be treated as if it was a single layer board.
You would need to run return path adjacent to each signal.
So you could have ground on the 4th layer if you choose too, but,
it doesn't make sense too if you have a ground already in one of the mid layers.

If a typical stackup is as following: there is a thick substrate between the middle plane.
there really isn't much of a difference for the two stack-up. You ought to have slightly better noise immunity and EMI shielding on the inner layer, though.
You haven't specified what flavour of signals you are dealing with; as long as it's not too exotic,a change like this can be ignored at all.